Packing Of Monosized Spheres Research Articles

Packing of Particles (Part 1)

Packing of monosized spheres in cylinders is examined as a function of particle/cylinder size ratio. For size ratios ranging from 1/25 to 3/4, the packing efficiency of particles inside cylinder was found to decrease linearly with the size ratio. Using geometric analysis, the amount of extra pore volume in the packed particle structure was found to depend linearly on the surface area of the cylinder as well as the size of the particle.

Packing of Particles (Part 2)

Packing of monosized fine spheres in the presence of monosized coarse spheres is examined both experimentally and analytically. By modeling the extra pore volume generated from the interaction of fine and coarse particles as a linear function of the size of the fine particles and the surface area of the coarse particles, good agreements between model and experimental data from the present study and those from literature were found. Good agreement was also obtained when the model was applied and compared with trimodal packing data. From these agreements, it can be concluded that the development of coarse/coarse particle contacts does not dramatically change the amount of extra pore volume. As a consequence, extra pore volume in dense packing of mixtures of narrowly distributed particles can be treated as dependent on the surface area of the desrupting media and the size of the particle.

Topological description of the densification of a granular medium

SUMMARYThe densification of a granular medium is described in terms of topological parameters. Two successive cases are quantitatively analysed starting from regular three‐dimensional (3‐D) packings (in continuous and digitized space) and simulated random 3‐D packings of monosized spheres.

Micromechanical modeling of powder compacts—II. Truss formulation of discrete packings

A numerical model for the constitutive response of powder compacts during densification is presented. Particle packings are treated as frameworks of links that connect the centers of particles through inter-particle contacts. The behavior of each link in the framework is based on unit problems for the interaction between individual spheres [ Acta metall. 36, 2551 (1988)]. This approach bridges the gap between unit models on the level of individual particles and the continuum behavior of very large packings of particles. Furthermore, since the model deals with individual particles, it is possible to predict the evolution of several details of packings that are important to the properties of the deformed part. Using this model the deformation of discrete powder packings under combined sintering and traction-induced compaction may be studied. Comparisons between model predictions and experimental data are presented for the sintering of a two-dimensional packing of mono-sized glass spheres. The model compares well with the experiment and is able to predict several microscopic features of the sintered packing.

A theoretical analysis of random packing densities of mono-sized spheres in two and three dimensions

A new approach using random triclinic primitive cells as the building blocks for three dimensional random packings is suggested. This can be used to investigate the geometric properties of random packings which are useful in sintering studies and in the study of structure of liquids and metallic glasses. This approach has been used here, to calculate the expected packing factors for two dimensional random arrays of equal sized circles and three dimensional loose and dense random packing of monosized spheres. The packing factors obtained in all cases are in excellent agreement with the values obtained experimentally, both by mechanical means and by computer simulation.

Derivation of pacticle size distributions from measurements on plane sections through particle beds. Effect of regularity of particle packing

When the size distribution of particles embedded in an opaque, continuous solid phase is required, the general approach is to deduce the distribution from the size distribution of particle cross-sections in a plane cut through the particle bed. When the particles are approximately spherical, this deduction can be performed by making the assumption that the distances from the plane of cut to the particle centers are rectangularly distributed. The validity of this assumption does not, however, appear to have been investigated in previously published work, and in the present contribution the assumption has been considered more closely. The distribution of the distances between the sphere centers and a random plane has been investigated both theoretically and experimentally, starting with regular packings of monosized spheres, and extending the treatment to monosized spheres packed at random and finally to packings of polysized spheres. The distribution of particle center to cutting plane distances will approach a rectangular distribution with increasing sample size even for strictly regular packings. However, for finite samples, the packing regularity may significantly affect the extent to which such a distribution is realized.

Radial voidage variation in randomly-packed beds of spheres of different sizes

Abstract The packing arrangement of the particles in a tablet die, before pressing, has no hitherto been considered as a variable in the tabletting process. Because of the complexity of this subject, the present investigation has been restricted to monosized and binary mixtures of spheres in a cylindrical container. The container could be revolved at speeds in excess of 1,000 rpm so that the thickness of an annular layer of water could be measured. From this, the voidage at any radial position could be found. The plot of voidage against distance from the cylindrical wall is a wave form which is damped out after about 5 particle diameters. For packings of monosized spheres the oscillations are regular. There appear to be two kinds of binary mixtures, those in which the particle sizes are similar, and those where the diameter ratio is greater than 0·4. The voidages calculated by suitably weighting the values for each component are in agreement with the measured voidages of the first kind but not with those of the second. Because there is an initial distribution of voidage, it is concluded that there must be some radial movement of the particles during the compacting operation.